My suggestion is actually incredible simple minded, but I felt it's not been approached properly before.

Add some more signature options to the gift message. For example, I wanted to gift my girlfriend a game and found out I did not have a "Love, XXXX" option or something along those lines.

The gamer signatures are cool and all, but still I feel there should be something more standard complimenting the "best wishes" option. It feels too weird to gift something to my GF or my grandma or whatever and sign it with "XOXOXO" or "Buckle up!".

It's a silly idea and by no means a high priority one, but I thought it would be nice to mention it.